Rosen didn't back down this morning in an interview on CNN, as she tried to explain that the issue isn't about stay-at-home moms vs. mothers who work outside of the home. She said Republicans who are criticizing her are trying "to change the subject" from Mitt Romney's record.

"The issue here that I'm focusing on is ... Does Mitt Romney have a vision for bringing women up economically and can he himself stop referring to his wife as his economic surrogate."

Ann Romney, in a separate interview on Fox News, defended her husband's record and said her choice to stay at home and raise her five sons should be respected.

"My career choice was to be a mother," Romney said today. "We have to respect women and all those choices they make."

Rosen's original comments, made during a CNN interview Wednesday night, immediately drew rebukes from several top Democrats working on President Obama's re-election campaign, including campaign manager Jim Messina, strategist David Axelrod and deputy campaign manager Stephanie Cutter.

Messina tweeted: "I could not disagree with Hilary Rosen any more strongly. Her comments were wrong and family should be off limits. She should apologize."

With his eye on the general election, Mitt Romney is now working to erase a huge gender gap. A recent USA TODAY/Gallup poll of 12 swing states showed President Obama leading Romney by 18 percentage points among women voters.

Ann Romney has emerged as one of her husband's most effective surrogates on the campaign trail, and she has spoken often of how women have told her they have concerns about the economy.

Rosen made her comments about Romney last night on CNN, for which she is also a contributor. Here's what she said:

What you have is Mitt Romney running around the country, saying, 'Well, you know, my wife tells me that what women really care about are economic issues, and when I listen to my wife, that's what I'm hearing.' Guess what? His wife has actually never worked a day in her life.

Rosen, a partner in a political communications firm, is the mother of twins. She is a longtime Democratic strategist and is perhaps best known for her tenure as head of the Recording Industry Association of America, the music industry's trade group, from 1994 to 2003.

She also took to Twitter last night to try and explain her comments, at one point saying she meant that Romney "never had to care for her kids and earn a paycheck like most American women."

USA TODAY/Gallup poll to Romney: "Please know, I admire you. But your husband shouldn't say you are his expert on women and the economy."